Task #1: comparing phone plans plus telecommunications offers a plan of $20 per month for an unlimited calling and data plan and 10 cents per text message sent. talkmore, a competing company, offers a plan of $55.00 per month for an identical unlimited calling and data plan and five cents per text message. how can you determine which plan will be cheaper for you?

Let x represents the number of messages and y represents the total cost.

Thus, According to the question,

For, First company,

y = 20 + 0.1 x    --------------(1)  ( since, 1 cent = 0.1 dollars )

For second company,

y = 55 + 0.05 x   ---------------(2)

By solving equations 1) and 2),

We get,

x = 700 and y = 90

Thus, we have three conditions,

Condition 1) For x < 700,

20 + 0.1 x  >  55 + 0.05 x

Before 700 messages, the cost of plan (1) is cheaper than plan (2).

Condition 2) For x = 700

20 + 0.1 x  =  55 + 0.05 x

⇒ for 700 messages both plan have the equal cost of $ 90.

Condition 3) For x > 700

Since, The slope of line (1) = 0.1 ( after comparing with the general equation of line y = m x +c, where m is the slope of the line)

Similarly, the slope of line (2) = 0.05

Since, 0.05 > 0.1

the slope of line 2) is less than the slope of line 1)

⇒ After 700 messages the cost of plan 2) will be cheaper than that of plan 1).

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

27 +27 or 27times 2=54

the diffrence is 0